To determine which expression for A results in a true equation with \( A = 5 - \frac{11}{3} \), let's first compute \( 5 - \frac{11}{3} \).
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Convert 5 to a fraction with a common denominator of 3: \[ 5 = \frac{15}{3} \]
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Now, calculate \( 5 - \frac{11}{3} \): \[ 5 - \frac{11}{3} = \frac{15}{3} - \frac{11}{3} = \frac{15 - 11}{3} = \frac{4}{3} \]
So, \( A = \frac{4}{3} \).
Next, let's evaluate each given expression to see which one is equal to \( \frac{4}{3} \):
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\( A = \frac{15}{3} + \frac{1}{3} \) \[ A = \frac{15 + 1}{3} = \frac{16}{3} \]
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\( A = 1 \frac{2}{3} - \frac{1}{3} \) \[ 1 \frac{2}{3} = \frac{5}{3} \] \[ A = \frac{5}{3} - \frac{1}{3} = \frac{5 - 1}{3} = \frac{4}{3} \]
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\( A = -1 \frac{2}{3} + \frac{1}{3} \) \[ -1 \frac{2}{3} = -\frac{5}{3} \] \[ A = -\frac{5}{3} + \frac{1}{3} = -\frac{5 - 1}{3} = -\frac{4}{3} \]
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\( A = 1 \frac{2}{3} + \frac{1}{3} \) \[ A = \frac{5}{3} + \frac{1}{3} = \frac{5 + 1}{3} = \frac{6}{3} = 2 \]
After evaluating all expressions, we find that the only expression that equals \( \frac{4}{3} \) is:
\( A = 1 \frac{2}{3} - \frac{1}{3} \)
Thus, the true equation is:
\[ A = 1 \frac{2}{3} - \frac{1}{3} \]
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